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Formation of Ad-Layers and Clusters on Condensation of Metal Vapors on Solid Surfaces.

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Formation of Ad-Layers and Clusters on Condensation of Metal Vapors
on Solid Surfaces[**]
By Rolf Niedermayer"]
Synthesis of organometallic materials can be accomplished in many cases by cocondensation
of metal atoms and organic molecules at low temperatures. The reaction kinetics is determined
by the competition between metal cluster growth and formation of the organometallic compound.
Interesting compounds may contain one or more metal atoms; the latter type could be obtained
by reaction between a cluster containing the desired number of metal atoms and an organic
molecule. A precise knowledge of the events occurring on condensation of metal atoms and
cluster formation can therefore be of value in the control of chemical synthesis. These phenomena
have been investigated in connection with the study of the growth of thin metallic films,
both experimentally and theoretically. Direct observation of the formation of very small clusters
is difficult. The good agreement between experimental results and recent calculations for the
development of large clusters, however, allows reliable theoretical conclusions for the first
stages of adsorption and cluster formation. The present contribution describes experimental
work on film growth and relevant theoretical concepts, and an attempt is made to develop
applications to organometallic synthesis.
1. Introduction
The common point of interest between the physics of thin
films and low temperature condensation as a synthetic
method''] is the fate of a single atom on a solid surface.
Only one method provides a direct answer to this question:
field ion microscopy. It can conveniently be used for the
direct observation of condensation, as well as subsequent
diffusion, desorption, or possible cluster formation. However,
the conditions of observation are severely restricted and the
utility of the method consequently restricted. We therefore
have to rely on more indirect methods if we wish to vary
the experimental conditions over a wide range.
Those stages of condensation, in which coherent layers
or extended clusters have already been formed, can easily
be observed by electron microscopy or electron diffraction
under a great variety of conditi~ns[*-~l,
and it has become
possible to analyze these experiments q~antitatively'~,
'I.
Examples of the experimental and theoretical results cited
in this report will give an impression of the state of the
art. The quality of these results for later growth stages permits
conclusions to be drawn for the early stages, and thus provides
an insight into the history of the individual condensed atom.
This insight can be summarized by a number of simple mathematical expressions which conclude the present discussion.
2. Two-Dimensional Growth
An understanding of condensation phenomena requires that
a distinction be made between a number of binding energies:
A. the evaporation energy of the adsorbate, for example of
the adsorbed metal, characterizes the binding of the metal
atoms to one another. The energy required to separate a
metal atom from a surface is known as the desorption energy
['I
Prof. Dr. R. Niedermayer
Institut fur Experimentalphysik IV der Universitat
463 Bochum. Postfach 2148 (Germany)
[**IBased on a lecturedelivered at the symposium "Metal Atoms in Chemical
Synthesis" held under the auspices onf the Merck'sche Gesellschaft fur Kunst
und Wissenschaft e.V. at Darmstadt (May 12-15, 1974).
212
(Edes). Finally, a certain activation energy has to be expended
to move an adsorbed atom from one binding site to another,
i.e. the migration or diffusion energy (&iff).
Metal atoms condensed onto other metal atoms or onto
semiconductors are often bound with a high desorption energy of the order of magnitude existing between the metal
atoms. The desorption energy on ionic crystals, e.g. alkali
halides, is somewhat lower, approximately 20 kcal/mol, while
the binding of metal atoms to graphite or similar substrates,
and probably to noble gases, is weaker, the desorption energy
being about 6 10 k c a l / m ~ l [ ~ - ~ ] .
These differences in binding energy essentially determine
the mode of film growth. It can in fact be shown that threedimensional cluster formation is preferred if the binding
between the metal atoms themselves is much stronger than
their binding to substrate. Theoretical consideration^'^* lead
to the following condition for three-dimensional cluster formation:
while two-dimensional clusters form if
In intermediate cases the growth will be two-dimensional
or three-dimensional, depending on the geometry of the lattices
of substrate and film.
These general rules predict that metals on metals or semiconductors have an initial tendency to grow in two dimensions.
In some instances this two-dimensional growth continues to
form thicker films, but in most cases growth changes to the
three-dimensional mode after completion of the first few monolayers.
An example of purely two-dimensional growth up to 80
ML (monolayers)currently being investigated by M[j~nczak[~]
will now be discussed. Ultrahigh vacuum and cleanliness of
the substrate are absolutely essential if reliable conclusions
are to result from investigations of this kind. In this experiment
sodium is evaporated slowly onto a tungsten (100) surface.
Angew.Chem. inremar. Edit. f Val. 1 4 (19751 1 N o . 4
The number of condensed atoms, the structure of the film,
the desorption energy, and the frequency constant of desorption can be determined independently in each individual experiment. Under certain conditions the diffusion energy can also
been measured. All these data are necessary for analysis of
a growth experiment, but in most cases they are not available
at the same time.
Condensation of sodium at a rate of 10l2 atoms/cm2s onto
tungsten at 370°K leads to saturation after deposition of
5 x l O I 4 atoms/cm2 (Fig. 1). The structure of this film has
been investigated in situ by grazing incidence high energy
I
electron diffraction (RHEED) which affords diffraction patterns like that in Figure 2.
Both the diffraction pictures of the substrate and those
of the film show elongated streaks perpendicular to the substrate and are characteristic of diffraction by two-dimensional
structures. The Na-covered surfaces show additional streaks
in the [ l l O ] azimuth. This provides an indication of the positions of the Na atoms, as shown in Figure 3.
I
05
OL
03
Fig. 3. Model of the sodium-covered tungsten surface as derived from the
diffraction pictures.
I
0
01
rn
0
1
Op
03
2
0,5
0,L
3
4
7tIMSl-
5 7tnhli~l-
Fig. 1. Dependence of the number of sodium atoms fled, adsorbed on a
W(100) surface upon the number y.r of atoms presented to the substrate.
Impingement rate y = 9 x 10" atoms c m - 2 s - 1 (0.06 ML min-I); substrate
temperature, 370°K.
c 100 1
c1101
w- 11001
w - 11001~ 1 2 x 2 Na
1
Thesodium atoms are seen to form a superlattice on W(lOO),
which consists of a centered square mesh whose edge is exactly
twice as long as that of the underlying tungsten surface. This
means that the distance between the sodium atoms is about
4% greater than in the lattice of the compact material. The
number of atoms per cm2 in this configuration is precisely
5 x I O l 4 atoms. Comparison with the deposition experiment
of Figure 1 shows that saturation occurs after completion
of the above structure, i.e. that the desorption energy then
falls. Similar observations are made in many other cases of
metal film
The energy of desorption is Edcr=2.5 k0.2
eV, while the heat of evaporation of sodium is only 1.09
eV. According to eq. (2), this ratio of binding energies must
lead to two-dimensional growth. At lower temperatures, e.g.
310"K, further growth proceeds linearly with time and remains
two dimensional. The diffraction pictures still show streaks
and remarkably, indicate no relaxation of the lattice constant
to its bulk value up to 80 ML. Corresponding diffraction
patterns are shown for 20and 80 ML in Figure 4. The distortion
of the lattice of the film up to relatively large thicknesses,
i.e. real pseudomorphic growth, is a rather singular result
of this investigation. It can be understood from the plot of
the desorption energy as a function of thickness, shown in
Figure 5. We have already stated that the first monolayer
20 ML
80 ML
Fig. 2. Diffraction pictures of a clean W(100) surface in the [lo01 and the
[110] azimuths, and of a W surface covered by 5 x
Na atoms cm-2.
The lower part of the figure shows a drawing of the reciprocal mesh of
the sodium-covered surface.
Angew. Chem. internat. Edit. 1 Vol. 1 4 ( 1 9 7 5 )
No. 4
w
Fig. 4. Diffraction pictures of a W(100)surface covered by 2 x 1016 and
Na atoms c m - 2 (T= 310°K).
8x
213
is adsorbed with a binding energy of 2.5 eV. The next layer
is bound with 1.27 eV-as is apparent from Figure 5-and
then the binding energy decreases monotonously to 1.06 eV,
which is attained after 4 monolayers and corresponds approximately to the bulk evaporation energy of sodium. A layer
of minimum binding energy would permit lattice relaxation
via two-dimensional dislocations. However, no such layer is
present in our example, and so relaxation must be severely
impeded" ''I. The ?a layer therefore remains strained, like
a sheet of rubber stuck under tension to a piece of wood.
W-(OOI) /11101
W-(OOl) / r1007
'8
K-(110) / 17111
m
Fig. 6. Diffraction pictures of a clean W( 100) surface and of three-dimensional
potassium clusters grown on this surface.
10
m
L,,,5
10
20
30
40I
50I
O
60i
nldr c 10" cm? I
Fig. 5. Dependence of the desorption energy of sodium from tungsten on
the number of deposited sodium atoms.
3. Three-DimensionalGrowth
To our knowledge the example of extreme two-dimensional
growth in Section 2 is the only known case of extended
pseudomorphism, and should be considered as a limiting case
of film growth. Incorporation of two-dimensional dislocations
in an intermediate layer usually ensures early relaxation of
the layer lattice. However, early transition to three-dimensional growth is more common, and can be particularly
well demonstrated for an example studied by Steinhage"!
Steinhage also investigated growth of an alkali metal, i.e.
potassium, on W(100),using the same equipment but somewhat
less refined. The potassium films start to grow two dimensionally in exactly the same way as Na films. The binding
energy of the first monolayer is higher than that of the second.
The structure of both layers corresponds to Figure 3. However,
the third monolayer has a different structure and is much
more weakly bound. The desorption energy falls to about
10% ofthe bulk evaporation energy of potassium after completion of the third monolayer, and further growth proceeds
via three-dimensional clusters. The lattice parameters of these
dusters agree with the bulk lattice constants. The diffraction
pictures of the final structure are shown in Figure 6; the
appearance of spots instead of streaks indicates three-dimensional diffraction, i.e. clusters. Compensation between the first
two strained layers and the unstrained clusters must take
place via an arrangement of two-dimensional dislocations in
the interface. It appears significant that the change in the
mode of growth occurs precisely when the binding energy
has a minimum value.
Very similar results can be obtained in experiments on
the growth of many metals on other metals or on semiconductors. However, these systems d o not permit accurate determination of the number of clusters, and recourse is generally taken to the growth of metals on alkali halides for
214
investigations on cluster formation and nucleation. In these
experiments the cluster layer is fixed in a thin amorphous
carbon film and the substrate then dissolved. The carbon
films are subsequently investigated by transmission electron
microscopy to measure of the number and size of nuclei.
Typical examples are the growth experiments for Au on NaCl
conducted by Robins et
1 4 ] . Figure 7 shows a series
of electron micrographs of the nucleation and coalescence
of gold clusters on a (100) rock salt face at a condensation
rate of l O I 3 c m - 2 s - 1 and a substrate temperature of 250°C.
Nucleation is homogeneous, apart from a few steps of the
substrate. The nuclei are partly oriented in prefeiential directions; their number passes through a maximum and then
decreases slowly owing to coalescence. The particles are
approximately 150A in diameter at the time of maximum
nucleus density. Evaluation of such micrographs reveals the
dependence of the number of nuclei upon time (Fig. 8). The
rm
Fig. 7. Electron micrographs of clusters in various growth phases (Au on
NaCl (100) surface).
Angew. Chem. internat. Edit.
Vol. 14 ( 1 9 7 s ) J No. 4
increasing curve (short time scale) corresponds to the end
of the nucleation stage while the decreasing curve (long time
scale) represents the coalescence stage.
Thus the nucleation rate N c , the saturation concentration
NC,FI1,,
and the cluster size can be measured as a function
of time t , substrate temperature 7; and impingement rate
J,,,.
These results can be understood quite well in terms
of a kinetic theory of cluster growth, and lead to conclusions
about the initial stages of growth.
rot
m
0
0
10
1
20
2
30 LO 50 60 70 80 90
3
L
5
6
7
8
9
1
-
100
0
t [mini
Fig. 8. Evaluation of the growth experiment of Fig. 7. Dependence of nucleus
density upon deposition time ( x , short time scale; , long time scale).
Impingement rate y = 10” atoms cm-’s-’ ; substrate temperature, T= 523°K.
where Bi*+I is the smallest stable cluster;
the number of atoms condensed in the stable clusters
N. =
X
i.11,
i=i*+I
1
and the mean cluster size
from which the mean cluster radius can easily be derived.
Numerical solution of eqs. (4) is in fact possible. The only
data required for such calculations are the binding energies,
the lattice parameters, substrate temperature, and impingement rate. Figure 9 shows the detailed results for the case
of gold on a rock salt substrate at 573 “K and an impingement
rate of 10l3cm-’ s - ’ . The desorption energy (Edes= 20 kcal/
8.5 kcal/mol) have been
mol) and the diffusion energy (&ill=
chosen for best agreement with a wide range of measurements.
Under such conditions the growth process is governed by
the equilibrium between impingement and desorption, which
is indicated by a constant value of monomer concentration
for a considerable time interval. The stationary value determined by impingement rate J,,, and desorption probability
a d e s is
4. Kinetic Theory of Cluster Growth
Cluster growth can be analyzed with the aid of a fundamentally simple kinetic theory. A brief account of this theory
will be followed by a discussion of the results obtained for
the growth of gold on rock salt, which permits a comparison
with experiment (Section 3).
Cluster growth has attracted much theoretical attention
during the last decadef4-’], most of the work being based
on a model of a sequence of molecular reactions. Monomers B
react with i-atomic polymers B,.
The decay probabilities ai+ can be calculated from thermodynamics, and the growth probabilities J i by solution of the
diffusion problem“ I 61. The complete polymerization process
can be described by a set of differential equations:
’.
(4)
ii,=J,-]n,- I-(J,+a,)n,+?i+~n,+~
The growth probabilities depend on all polymer concentrations and the size of the growing polymer, while the decay
probabilities depend on the properties of the decaying polymer
and on temperature only. In connection with this theory a
polymer will be called a “cluster”. If the set of equations
(4)can be solved then all experimentally important quantities
can be easily derived. These quantities are: the total number
of stable clusters
A n g r w . Chrm. inrwnar. Edir. / Vol. 1 4 ( 1 9 7 5 )
1 No. 4
@ag
-5 - L
- 3 -2 -1
0
1
2 Igt-
Fig. 9. Calculated dependence of some cluster concentrations n,. the total
number of stable clusters N,, and the number of condensed atoms N., on
deposition lime. Number ofatoms presented to the substrate J , , , . t at deposition rate J , , , is also shown.
The induction period before the start of nucleation is lO-’s
and the nucleation ends by coalescence after 100 s; the maximum number N,c,,l, of clusters is reached after 1OOOs. The
nucleation period is characterized by a linear increase in the
number of clusters N,. Another result that can be obtained
from the theory concerns the size of the critical nucleus, i.e.
of that cluster which is just more likely to grow than to
decay under the conditions of the experiment. In this case
the first stable cluster is a trimer. Each class of clusters has
its own induction period; the rise of the cluster concentrations
is steeper the larger the cluster. The number N , of condensed
21s
atoms increases with t2 during the nucleation period, and
then becomes linear. This is in general agreement with experiments on retarded condensation'' 'I.
Unfortunately, the observation of the time dependence of
film growth is limited to the final stages of the nucleation
period (Fig. 8). This makes a direct comparison of experiments
with the theoretical results (Fig. 9) difficult. However, the
dependence of nucleation rate, saturation concentration, and
mean radius at saturation upon temperature and impingement
rate permits comparison of the properties of cluster growth
with experiment over a wide range of conditions. Figure 10
shows the influence of the impingement rate on the above
parameters. The plots of the nucleation rate N c are almost
linear over a wide range of impingement rates, and the slope
is 2<d(ln N,)/d(lnJi,,)<2.5. The size of the critical clusters
is given alongside the curve plotted for 834°K. The influence
of the critical cluster size on N c is much less pronounced
than, e.g., on nucleation of mist droplets because nucleation
in film growth is determined by surface diffusion to a far
greater extent than by the decay equilibrium. The dependence
of the saturation concentration and the mean radius upon
impingement rate is much weaker than that of the nucleation
rate. Figure 11 shows the temperature dependence of film
growth. At high temperatures the saturation concentrations
of clusters decrease and the mean cluster size increases. This
is of practical importance for the reduction of crystal defects
in thin films. A comparison of experimental data obtained
by Robins er u / . [ ' ~ I with theoretical results is shown in Figure
12. The dependences of nucleation rate and saturation concentration upon impingement rate (at 300°C) and substrate temperature (at 10l3 c m - 2 s - ' ) agree within the experimental
scatter of data.
---
m
103 i T
Fig. I I . Logarithmicdependenceof characteristic film parameters on substrate
temperature 7 for some impingement rates. Legend a s in F l g . 10.
Fig. 12. Comparison between theoretlcal results for the growth of gold on
a substrate with Ede.=20 and Edat==8.5kcal/mol and experimental growth
data for gold on rock salt (points from [13. 141).
5. Low Temperature Condensation
kl Jlmp
-
Fig. 10. Logarithmic dependence of characteristic film parameters on impingement rate J,,,for some temperatures. N,,.,,, is the saturation nucleus concentration, fi, the nucleation rate, F.,,, the mean cluster radius at the time
of saturation (in cm). n* is the size of the critical nucleus at the points
indicated.
This indicates that numerous growth experiments can be
described by a kinetic theory. Extrapolations to experimentally
unobservable regions therefore seem justified.
216
Two examples of low temperature condensation will be
presented: condensation of gold at 80°K and an impingement
rateof 1 0 ' h c m - 2 s - ' on substratescharacterized by (i) Edes=5
and EdifT=2 kcal/mol and (ii) Edes=10 and Ed,ff=4 kcal/mol.
These substrate data might be representative for physical
adsorption of a metal on a solid noble gas surface. Accurate
experimental data are not yet available.
The low binding energy case is shown in Figure 13. The
desorption equilibrium described by eq. (8) is not attained.
Instead the monomer concentration is limited by twin formation before significant desorption can occur. The cluster concentrations and nucleus concentrations rise very steeply. No
nucleation period, N,- t , is observed. The growth under such
conditions can be described by an induction period of 10- s,
twin formation until
s, growth of the almost constant
number of nuclei until l o - ' s, then coalescence. Diffusion
is the governing feature of this mode of growth.
Both cases together are shown in Figure 14. In the high binding energy case diffusion of the monomers is largely restricted and film formation occurs directly by coalescence without
involving clusters. The induction period is 10-2s. This mode
Aiigen-.
Chrm. inrrrnar. Edit. I Vo1. 14 ( 1 9 7 5 ) 1 No. 4
16.
15IL.
//
r,,
The maximum concentration of monomers is attained at
T 3 .T, and its value is
At this time the numbers of twins and monomers are approximately equal. These formulas can be used as guidelines for
the choice of rates, temperatures, and substrates for the attainment of a certain monomer concentration at a given time.
6. Final Remarks
Fig. 13. Calculated dependence of cluster concentrations on deposition time.
Legend as in Fig. 9. The calculations are for the case of weakly bound
gold (Edp.=% Ealti=2 kcal/mol) o n a substrate at 80°K.
T = 4 J,mp"z
exp IEdlIl / 2 k l 1
A systematic experimental and theoretical investigation of
cocondensation of metals and noble gases and organic materials at low temperatures is still unavailable. Extensions of
theoretical considerations delineated above should, however,
not be too difficult.
Meanwhile some conclusions can be derived from the simple
one-component condensation theory. If the metal atoms react
with the cocondensing atoms, a new substrate will be formed,
generally with a new diffusion energy. Whatever this may
be, a suitable surface temperature and rate of impingement
can always adjust the induction time T and the monomer
concentration at this time to optimum values for a reaction
with single metal atoms:
Whether reproducible reactions with dimers, trimers, or higher
polymers can be achieved experimentally or whether the conditions for such reactions can be deduced theoretically must
remain the object of future investigations.
energy of sublimation
energy of desorption
energy of difhsion
substrate temperature
Boltzmann constant
impingement rate
desorption probability
time
symbol for a cluster of i atoms
concentration of clusters B;
growth probability of a cluster B,
decay probability of a cluster Bi
total concentration of stable clusters
number of condensed atoms
nucleation rate
critical cluster size
mean cluster size
saturation concentration of stable clusters
mean cluster radius
mean cluster radius a t saturation
stationary monomer concentration at desorption equilibrium
maximum monomer concentration
induction time
distance between adsorption sites
diffusion frequency
cross-section for twin formation
Fig. 14. Calculated dependence of cluster concentrations on deposirion time
for two different cases of binding. -,
binding as in Fig. 13:
binding
with ECI,,= 10 and Ed,rl= 4 kcal/mol. The induction time T and the maximum
monomer concentration as calculated from eqs. (9) and (11) are also indicated
for the two cases.
----.
of growth also gives two-dimensional layers, which are however strongly disordered compared to those described above.
The foregoing example of low temperature condensation
may be of interest for chemical synthesis, especially in the
case of reduced surface migration. Simple formulas permitting
rapid assessment of growth can be derived from the general
theory for the low temperature case, i.e. the case where twin
formation dominates over desorption. Thus the induction time
is
Received: July 29, 1974 [A 49 IE]
German version: Angew. Chem. 87, 233 (1975)
The square root generally lies between 1 and 10 cm-'
The concentrations of monomers and twins at the end
of the induction period are
sliZ.
Angew. Chem. inturnur. Edit. f Vol. 14 ( 1 9 7 5 )
/ No. 4
P. L. 77nims, Advan. Inorg. Chem. Radiochem. 14, 121 (1972): J. Chem.
Educ. 49. 7x2 (1972): Angew. Chem. 87, 295 (1975): Angew. Chem.
internat. Edit. 14. 273 (1975).
[ 2 ] H. Mayer in H. G. Schnridrr and V R u t h : Advances in Epitaxy and
Endotaxy. Deutscher Verlag fur Grundstoffindustrie, Leipzig 1971, p.
63.
[I]
217
[3] R. Niederma.wr, Krist. Tech. 5 , 2 ( 1 970).
[4] Survey: J. A . Venables and G . L. Price in J . W M a t ~ h e w sEpitaxy.
:
Academic Press, New York 1975 (in press), Chap. 4.
[5] R. Niedermaj,er in H . G. Srhneider and K Ruth: Advances in Epitaxy
and Endotaxy. Deutscher Verlag fur Grundstoffindustrie. Leipzig 1974,
p. 21.
[6] A. Mlynczak, Dissertation, Universitat Bochum 1974.
[7] P. W Steinhage, Dissertation, Techiiische Universitat Clausthal 1969.
[S] H. Schmeisser and M . Harsdorff, Z. Naturforsch. 25a. 1896 (1970).
[9] H. J. Srowrll, Thin Solid Films 21, 91 (1974).
[lo] E. Bauir, Z. Kristallogr. Kristallgeometrie Kristallphys. Krlstallchem.
110, 372. 395 (1958).
[ I l l F. C . Frank and J . H. uan der Mrrwe. Proc. Roy. Soc. A 198, 205,
217 (1949).
[12] R. N i e d e r m a y r , Thin Solid Films I, 25 (1968).
[ I 3 1 V. N. E. Robinson and J . L. Robins, Thin Solid Films 20, 155 (1974);
and literature quoted therein.
1141 A. J. Donohoe and J . L. Robins, J. Cryst. Growth 17. 70 (1972).
[15] V Halprrn. 1. Appl. Phys. 40, 4627 (1969).
[16] K. J. Routledge and H . J . Sfowell, Thin Solid Films 6, 407 (1970).
[I71 A . HBlting, Dissertation, Technische Universitat Clausthal 1969.
Production and Condensation of Metal Vapors in Large Quantities[**]
By Walter Reichelt"]
1. Introduction
Table 1. Temperatures at which the metals listed have a vapor pressure
of 1 tom.
Anybody working with evaporation or sputtering of metals
under reduced pressure knows that chemical reactions can
occur between the vaporized metals and organic components
present in the residual gases. Such vapors arising from paraffin
oils for instance may enter the working chamber if baffeling
between diffusion pump and chamber is poor. The products
can often be recognized by their smell.
Reactions of this kind have their uses, however, and when
performed on a production scale they require efficient sources
of metal vapors. Some aspects of these sources will be considered in the present report.
Metal
T
c11
Ti
Cr
Mo
W
Fe
Ni
~
1578
3118
~
1798
2 730
co
-
Pt
2 646
C"c1
PI
r31
2180
1610
3 300
3 980
1780
I 800
1910
2 600
2 191
1695
3 280
3 874
1790
1408
1471
2531
w
Ta
h
Re
2. Binding Energy and Evaporation Rates
Many practical applications require a knowledge of the
evaporation rate, a quantity deriving from the binding energy
of the metal. Macroscopic material constants depending upon
the binding energy include the melting point and the heat
of evaporation. If we have reliable values of the heat of evaporation of a metal, then vapor pressures can be calculated for
any desired temperature. The vapor pressure values yield evaporation rates via the expression due to Hertz:
-
2000
sc
Y
a
z
Au
1000 -
cs
Rb
,
rn
30
20
60
50
40
z+
#
70
I
80
Fig. 1 Melting points m.p. wrsus atomic number Z
w
G : evaporation rate [g cm * SKI];p.: saturation vapor pressure; N : Langmuir
coefficient (approximately unity for most of the metals encountered in practice
when evaporated from the melt)
II
~
Vapor pressure values reported in the literature sometimes
show considerable variations. An estimation of the errors
can draw upon the theory of metal binding energies. Table
1 lists the temperatures at which the vapor pressure of a
number of metals warranting interest in this connection
amounts to 1 torr; the melting points and heats of sublimation
are given in Figures 1 and 2.
[*I Dr. W. Reichelt
W. C. Heraeus GmbH
645 Hanau, Postfach 169 (Germany)
[**I Based on a lecturedelivered at the symposium "Metal Atoms in Chemical
Synthesis" held under the auspices of the Merck'sche Gesellschaft fur Kunst
und Wissenschaft e.V. at Darmstadt (May 12-15,1974).
218
V
sc
Ca
rn
20
Sr
Rb
30
Cd cs
50
LO
I
60
70
80
2-
Fig. 2. Heats of sublimation uersus atomic number 2.
Angew. Chem. internat. Erlif. 1 Vol. 14 ( 1 9 7 5 )
1 No. 4
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